Paradoxical Evidence

Please enlighten us Don.

no problem,

In probability and statistics, this paradox, or effect, is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data.

This result is often encountered in medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations. The Paradox disappears when causal relations are brought into consideration.

Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as this paradox. Hence my altruistic post !!

Muggins (not his real name) first described this phenomenon in a technical paper in 1951

The other example I have to hand is a real-life example from a medical study comparing the success rates of two treatments for kidney stones. You are probably more familiar with that one ?

Idiot's guide to Simpson's  Paradox!

 The table of statistics upon which my initial post was based

Is there a link to the tutors evidence to the campaigners?

Berkeley gender bias case

One of the best-known real-life examples of Simpson's paradox occurred when the University of California, Berkeley was sued for bias against women who had applied for admission to graduate schools there. The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.

But when examining the individual departments, it appeared that no department was significantly biased against women. In fact, most departments had a "small but statistically significant bias in favor of women." The data from the six largest departments are listed below.

The research paper by Bickel et al. concluded that women tended to apply to competitive departments with low rates of admission even among qualified applicants (such as in the English Department), whereas men tended to apply to less-competitive departments with high rates of admission among the qualified applicants (such as in engineering and chemistry). The conditions under which the admissions' frequency data from specific departments constitute a proper defense against charges of discrimination are formulated in the book Causality by Pearl.

The above is an abstract from Wikipedia. The figures in my initial post illustrate a very similar situation and I simply built a similar "story" behind my own figures. If you type "Simpson's Paradox" into Google you will get the Wikipedis link containing the above abstract and a whole lot more.

Hope that helps you Jota ?

Tony's link above, describes Simpson's Paradox very clearly.

The moral of the story ? think very, very carefully when dealing with statistics and remember.....

95% of the people who died last year in England had eaten tomatoes......

Next............

statistical blind testing of interconect cables in hifi featuring Naim HiLine, Chord STA, Vertere, both "out-of-the-box" and following 600 hours "burn-in".................

Also, "Cum hoc ergo propter hoc" is a well established logical fallacy.  Association does not prove causality...there is often more to the story.

"Statistics don't lie, but liars can figure."

"There are lies, damn lies, and statistics."

A bit of fun and light reading...

http://www.theatlantic.com/bus...ee-the-world/265147/

Don't take them too seriously  though!

Or as I also have heard, statistics don't lie, but liars use statistics.

I'll make them more relevant. Using the same data…

Rows are preamps. For each sex, the columns are : number of preamps purchased in a year, number that still had the preamp at a 5-y follow-up, and percentage of keepers.

Do women keep their preamps more than men ? What is your recommendation to Naim's marketing department ?

That answers the second question. Any thoughts on the first ?

Thanks very much Don! 

I suspect many of the more headline grabbing statistics can be explained in this way.